Ultimate derivation unclear. Theories include an alteration from 口広 (kuchibiro) in reference to the wide mouth;[1] an alteration from 口開く (kuchibiraku) in reference to the gaping mouth; and an alteration from 黒白 (kuroshiro) in reference to the black-and-white coloration of certain cetaceans.[2]

However, the oldest sources clearly spell the term as kudira.

This rules out 口(kuchi, ancient kuti, “mouth”) as an etymon, as the oldest compounds using this term use the bound form kutu, not kuti, and there is no support for a kutu → kudi shift.

This also rules out 白(shiro, shira, ancient readings siro, sira, “white”) as an etymon. Although rendaku (voicing in compounds) would give modern jira as a reading for 白, the ancient reading of sira would voice to something closer to zira, and there is no support for a zira → dira shift.